In parallelogram PQRS, find the height h. Then calculate the area of PQRS.

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In parallelogram PQRS, find the height h. Then calculate the area of PQRS.

Mathematics
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In a paralleogram, what do you know about opposite angles?
|dw:1437449376951:dw|
@mathstudent55 ∠R=45, ∠S=180-45=135, ∠P=45,and ∠Q=135.

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Correct. Opposite angles are congruent. |dw:1437450112404:dw|
That makes the small triangle on the left side a 45-45-90 triangle.
|dw:1437450166044:dw|
Since you have a 45-45-90 triangle, you can use the ratio of the length of the sides of a 45-45-90 triangle to find h.
Do you know the ratio of the sides of a 45-45-90 triangle?
1 to 1
\[\sqrt{2}\]
Yes, \(1 : 1 : \sqrt 2\) The hypotenuse is \(\sqrt 2\) times the length of either leg. The legs are congruent. The height of the parallelogram is the leg of the right triangle. What is the length of the leg?
8
Correct. Now you know the height of the parallelogram is 8. Do you know how to find the area of a parallelogram?
\(\Large A_{parallelogram} = bh\) where b = length of base, and h = height.
You were given a base of 20 cm, and you calculated a height of 8 cm.
A=bh. So A=20x8= 160cm^2
@SimiYami Do you understand how to find the area?
Yes, thank you for the help @mathstudent55. This is the exact answer in my book :D
You're welcome.

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